Question

At a local store, 65 female employees were randomly selected and it was found that their mean monthly
income was $625 with a standard deviation of $121.50. Seventy-five male employees were also randomly
selected and their mean monthly income was found to be $667 with a standard deviation of $168.70. Test the
hypothesis that male employees have a higher monthly income than female employees. Use α = 0.01.

Use any method, however, follow the PHANTOMS acronym.

P - Parameter Statement

H - Hypotheses

A - Assumptions & Conditions

N - Name the Test and state the curve you're using

T - Test Statistic - Round your value to TWO decimals and state the command you used to find this value

O - Obtain the P-Value or Critical Value . State the command you are using to find these values

M - Make a Decision about the Null Hypothesis and explain why

S - State Your Conclusion About the Claim

Answer 1

P-  male employees have a higher monthly income than female employees.

H-

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 <   0

A-

population is normally distributed

Sample are random and independent

N- 2 independent sample t test

T-

Sample #1   ---->   1          
mean of sample 1,    x̅1=   625.00          
standard deviation of sample 1,   s1 =    121.5          
size of sample 1,    n1=   65          
                  
Sample #2   ---->   2          
mean of sample 2,    x̅2=   667.000          
standard deviation of sample 2,   s2 =    168.70          
size of sample 2,    n2=   75          
                  
difference in sample means = x̅1-x̅2 =    625.000   -   667.0000   =   -42.0000
                  
std error , SE =    √(s1²/n1+s2²/n2) =    24.6287          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -42.0000   /   24.6287   ) =   -1.7053

O-

DF=133

p-value =        0.04523   [ excel function: =T.DIST(t stat,df) ]

M-

Conclusion:     p-value>α , Do not reject null hypothesis  
      

S- There is not enough evidence to conclude that male employees have a higher monthly income than female employees.

please revert for doubts and

please UPVOTE the solution